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Follow-up to previously answered impeller diameter question

Q: A few days ago, I posed this question: Q: I have a vessel with a top entering agitator without baffles. The vessel height is 2 m and vessel inside diameter is 1.5 m. The impeller type is three 60-degree pitched blades. Each blade has an inclination of 60-degress in respect to the agitator shaft too. The impeller diameter is 880 mm. The pitched blades are fixed to a cylinder that is 122 mm in height and with a 125 mm diameter. The width of the blade at the cylinder is 112 mm and at the end is 80 mm. The shaft diameter is 100 mm. The agitator has a velocity redactor of 1 to 10. The agitator has no driver and has no characteristics label. I want to use this vessel in the production of 50% calcium nitrate solution with a density of 1,450 Kg/cubic meters and a dynamic viscosity of 1.35-1.8 cp. What will be the calculated power at 180 rpm and 360 rpm?

I received this answer: A: The answer is don’t do it. There is no way an impeller that large should ever be rotated at 180 rpm in a vessel that size. Without baffles, the liquid contents would swirl over the top to the tank an splash everywhere around the tank. At 180 rpm, without baffles, the impeller power draw would be about 7.8 kW, that's kilowatts, not watts. At 360 rpm, the power jumps to 61 kW. The mixer described is suitable for a much larger tank, not for one 2 m tall and 1.5 m in diameter, regardless of the contents. Baffles only make the design >worse, because the power levels are about three times the levels without baffles. Do not attempt to operate the mixer in the manner described!

Of course, I am satisfied with the answer, but now I have a new idea. Can I do the blades of my impeller shorter, keeping up the original design, except the diameter? If I can do it, what would be the optimum impeller diameter to avoid having the liquid contents swirl over the top of the tank and splash? What would be the consumed power in this case? I attempted to calculate it, using the Perry’s Manual, but there wasn’t any similar impeller in the figure.

A: My understanding of the question and the process is:

The tank is 2 m in diameter and 1.5 m tall. The tank does not have baffles, but should have them for the density and viscosity described. I have assumed that the tank will contain about 3.75 cu m of liquid, with a viscosity of 1.8 centipoise and a density of 1,450 kilograms/cu m. The volume and physical properties are not critical within plus or minus 10% or 20%.

The previous question asked about a three-blade, pitched-blade turbine, 880 mm in diameter, with a 122 mm diameter hub and blades 122 mm wide at the hub and 80 mm wide at the tip. The blades are mounted at 60 degrees with respect to the shaft. Blade angle is usually measured with respect to the horizontal, so I have used information for an impeller with 30-degree angle (from horizontal) blades. Running this 880-mm diameter impeller at 180 or 360 rpm gave impossible results.

For the new question, asking about a smaller impeller, I have assumed that the smaller diameter impeller will be the original impeller with the blades carefully cut shorter. The blade lengths need to be cut to within about 2 or 3 mm radius of each other to keep forces balanced and the power draw even.

Without baffles the mixing intensity is quite limited. At 180 rpm, I would recommend an impeller diameter of 500 mm, which puts the blade width at the tip at about 106 mm. At those conditions the impeller will draw about 240 watts and should have about a 1 kW motor. At 360 rpm, the impeller should be only 350 mm in diameter, with a 113 mm blade width at the tip. The impeller will draw about 500 watts and again a 1 kW motor is reasonable. This impeller size at 360 rpm is rather small for the tank. However, the speed is high enough to give adequate mixing.

A much better design for this application would be for a tank with baffles. Typically, a tank has four baffles at 90-degree locations and about 200 mm wide. The mixing possible in a baffled tank is much better for this low-viscosity liquid and much less likely to splash out of the tank. At 180 rpm, a 650-mm diameter impeller would have a 99-mm blade width at the tip. The power input would be about 2 kW and provide three to four times as much mixing intensity as in the unbaffled tank. A 3.7-kW motor is suggested. At 360 rpm, a 450-mm diameter impeller with a 108-mm blade width would require about 4.2 kW. A 5.6-kW motor would be appropriate.

I believe that these recommendations should answer your questions and give you sufficient information to design and install a workable mixer.